For what values of a can you solve the linear system az + 3y = 2 and 4x + 5y = 6 by elimination without
multiplying first?
The values
and

Answer:

D

Step-by-step explanation:

3(25-(12))=39

3(13)=39

39=39

Answer:

This one is just 15+15+7+7 then divide by the preciptical

Step-by-step explanation:

add 15+15+7+7=44/2=22

Answer:

the answer is 117

sorry if wrong but that is what I got

Step-by-step explanation:

[tex] = - 39 \div \frac{1}{ 3} \\ [/tex]

[tex] = - \frac{39}{1} \times \frac{3}{1} \\ [/tex]

[tex] = - \frac{117}{1} \\ [/tex]

[tex] = - 117 [/tex]

Answer:

1.36 centimeters

Step-by-step explanation:

Given,

side length ( a ) = 17 mm

To find : Perimeter of regular octagon ( in cm )

Octagon has 8 sides.

Perimeter of regular octagon

= 8 x a

= 8 x 17

= 136 mm

1 mm = 0.1 cm

136 mm

= 136 x 0.1

= 1.36 centimeters ( cm )

Hence,

Perimeter of regular octagon is 1.36 centimeters.

Answer:

13.6 cm

Step-by-step explanation:

17 mm = 1.7 cm

Perimeter of octagon

= 8 x 1.7 cm

= 13.6 cm

walking tour is $15

boat tour is $18

Answer:

8y

Step-by-step explanation:

Answer:

[tex]\displaystyle \lim_{x \to 2} \frac{\sqrt{x + 7} - 3 \sqrt{2x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} = \boxed{ \frac{34}{23} }[/tex]

General Formulas and Concepts:
Calculus

Limits

Limit Rule [Variable Direct Substitution]:
[tex]\displaystyle \lim_{x \to c} x = c[/tex]

Limit Property [Multiplied Constant]:
[tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]

Limit Property [Multiplication]:
[tex]\displaystyle \lim_{x \to c} f(x)g(x) = \lim_{x \to c} f(x) \lim_{x \to c} g(x)[/tex]

Step-by-step explanation:

*Note:

The problem is too big to fit all work. I will assume that you know how to do basic algebra and calculus.

Step 1: Define

Identify given limit.

[tex]\displaystyle \lim_{x \to 2} \frac{\sqrt{x + 7} - 3 \sqrt{2x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}}[/tex]

Step 2: Find Limit (Algebriaclly)

Rationalize the function and apply basic limit techniques listed under "Calculus":

[tex]\displaystyle\begin{aligned}\lim_{x \to 2} \frac{\sqrt{x + 7} - 3 \sqrt{2x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} & = \lim_{x \to 2} - \frac{17(x - 2)}{\big( \sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5} \big) \big( \sqrt{x + 7} + 3 \sqrt{2x - 3} \big)} \\& = -17 \lim_{x \to 2} \frac{1}{\sqrt{x + 7} + 3 \sqrt{2x - 3}} \lim_{x \to 2} \frac{x - 2}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}}\end{aligned}[/tex]

[tex]\displaystyle\begin{aligned}\lim_{x \to 2} \frac{\sqrt{x + 7} - 3 \sqrt{2x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} & = - \frac{17}{6} \lim_{x \to 2} \frac{x - 2}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} \\\end{aligned}[/tex]

Let's now focus on just the rationalization of the function within the limit:

[tex]\displaystyle\begin{aligned}\frac{x - 2}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} & = \frac{(x - 2) \bigg[ (x + 6)^\Big{\frac{2}{3}} + 2 \sqrt[3]{x + 6} \sqrt[3]{3x - 5} + 4(3x - 5)^\Big{\frac{2}{3}} \bigg] }{\Big( \sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5} \Big) \bigg[ (x + 6)^\Big{\frac{2}{3}} + 2 \sqrt[3]{x + 6} \sqrt[3]{3x - 5} + 4(3x - 5)^\Big{\frac{2}{3}} \bigg] } \\& = - \frac{1}{23} \bigg[ (x + 6)^\Big{\frac{2}{3}} + 2 \sqrt[3]{x + 6} \sqrt[3]{3x - 5} + 4(3x - 5)^\Big{\frac{2}{3}} \bigg] \\\end{aligned}[/tex]

Substitute in the simplified function and continue:

[tex]\displaystyle\begin{aligned}\lim_{x \to 2} \frac{\sqrt{x + 7} - 3 \sqrt{2x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} & = - \frac{17}{6} \lim_{x \to 2} \frac{x - 2}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} \\& = \frac{17}{138} \lim_{x \to 2} \bigg[ (x + 6)^\Big{\frac{2}{3}} + 2 \sqrt[3]{x + 6} \sqrt[3]{3x - 5} + 4(3x - 5)^\Big{\frac{2}{3}} \bigg] \\& = \frac{17}{138} (12) \\& = \boxed{ \frac{34}{23} } \\\end{aligned}[/tex]

∴ we have evaluated the following limit without L' Hopital's Rule.

Step 3: Geometrical Interpretation

We can also graph the given function and approximate the limit. Please refer to the attachment for visualization.

___

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Answer:

  34/23

Step-by-step explanation:

The limit can be evaluated by simplifying the expression in such a way as to cancel the offending zeros.

__

Define the following (to help keep the algebra cleaner):

  [tex]a=\sqrt{x+7},\ b=3\sqrt{2x-3}\\\\c=\sqrt[3]{x+6}.\ d=2\sqrt[3]{3x-5}[/tex]

Then the desired limit is ...

  [tex]\displaystyle \lim_{x\to 2}\dfrac{a-b}{c-d}[/tex]

We observe that ...

  [tex](a-b)(a+b)=\underline{a^2-b^2}=(x+7)-(3^2(2x-3))=-17x+34=\underline{-17(x-2)}\\\\(c-d)(c^2+cd+d^2)=\underline{c^3-d^3}=(x+6)-(2^3(3x-5))=-23x+46=\underline{-23(x-2)}\\\\\displaystyle\lim_{x\to2}{(a+b)}=3+3=6\\\\\lim_{x\to2}{(c^2+cd+d^2)}=4+4+4=12[/tex]

In the following expression, the factors (x-2) cancel, so, our limit is ...

  [tex]\displaystyle\lim_{x\to2}\dfrac{a-b}{c-d}=\lim_{x\to2}\dfrac{(a^2-b^2)(c^2+cd+d^2)}{(c^3-d^3)(a+b)}=\lim_{x\to2}\dfrac{-17(x-2)(12)}{-23(x-2)(6)}=\boxed{\dfrac{34}{23}}[/tex]

The graph simply shows the distribution with the area corresponding to the information about the lawyer representing a Hispanic individual in a criminal trial.

A graph is a diagram showing the relation between variable quantities, typically of two variables, each measured along with one of a pair of axes at right angles.

Here, the probability that a juror is hispanic = p = 0.55 and the number of jurors = n =12

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-2.15

-2.154 should be your answer!! have a blessed day x

The relationship between the variable x and y will be linear. Then the correct option is A.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The graph is given below.

At x = 2, the value of y will be 6.

At x = 3, the value of y will be 4.

At x = 4, the value of y will be 2.

Then the relationship between the variable x and y will be linear.

Then the equation of the line will be

y = -2x + 10

Thus, the correct option is A.

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Answer:

last one

Step-by-step explanation:

after solving that, i got the same answer from the orginail one:

x=1,x=8

The proportion is equivalent to the original equation is (x+1)/2x = x²-7x+10 / 4x [option c]

Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

Given is an equation, 1/2 + 1/2x = x²-7x+10 / 4x

We need to determine the proportion equivalent to this,

So, taking the LHS,

1/2 + 1/2x

= 2+2x / 4x

= 2(x+1) / 4x

= x+1 / 2x

Hence, the proportion is equivalent to the original equation is (x+1)/2x = x²-7x+10 / 4x [option c]

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This is one of the many possible responses:

Different kinds of balls bounce to different heights when dropped on the same floor.

Sugar dissolves faster in hot milk than in cold milk.

Plants grow more slowly when they are not near a window.

One Opposite side pair of a trapezoid has equal length

A is true

<J is supplement to <K

JK and LM are not paralle

<J is congruent to <M may be true

May not be

Answer:

A.  [tex]\sf \overline{KL}[/tex] is parallel to [tex]\sf \overline{JM}[/tex]

D.  ∠J is supplementary to ∠K

Step-by-step explanation:

Properties of a trapezoid:

Although the sides of the shape do not have any arrows to indicate that any are parallel, we know that a trapezoid has one pair of parallel sides, so:

When two angles sum to 180° they are called supplementary angles.

As the two angles that are on the same leg sum to 180° then:

When added together the 4 angles need to equal 360

x = 360 -66-95-114

X = 85

Answer:

12 times

Step-by-step explanation:

first, find out how much she makes weekly.

40 (hours per week she works * 30 ($ she will earn per hour)

40 * 30 = 1200 per week

for 52 weeks so multiply that by her weekly pay

multiply her weekly pay (1200) by the weeks she works annually (52)

52 * 1200 = 62,400

she makes just $62,400 (annually, before taxes) with her new employer

subtract how much more money she needs

62,400 - 63,300 = -900

she needs 900 dollars

divide by the money she makes on weekends (for dog sitting)

900/75 = 12

she will need to dog sit at least 12 times to make approx. $63,300 annually, before taxes.

hope this helps:)

He had bank fees $15 that were not in his check register.

The correct option is (B)

Balancing statement is a final statement of your income tax liability for a tax year. It is issued by Revenue when your income tax liability has been reviewed and it shows: your total income from all sources. tax reliefs and credits claimed. amounts of income tax

Balance in check register be,

=Initial Balance - ( Expense on Food Market + Frank's auto parts + Barber shop ) + Deposit

Initial Balance = 900

Expense on Food Market= 67.25

Frank's auto parts =36.80

Barber shop =15

Deposit =650.45

So,

Balance = 900 - (67.25 + 36.80 + 15) + 650.45

              = 1550.45-119.05

             = $1431.40

Balance on Account statement be,

=  Opening balance - ( checks amount on different dates ) + deposit - fees

= 900 - (67.25 + 36.80 + 15) + 650.45  - 15

= 1550.45-134.05

= $1416.40

As, the balances in bank statement and in checking register are not matched. This is because the fees $15 paid on 9/30 is not calculated by Jerry in his check register

thus,

= $1431.40 - $15.00 (Fees)

= $1416.40

Now the balance on account and checking statements matched.

So, he had bank fees were not in Check Register.

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[tex]\huge\underline\mathsf \colorbox{cyan}{-1/2}[/tex]

Step-by-step explanation:

The equation of the graph is given by y = cos(0.4x) and has an amplitude of 1

An equation is an expression that shows the relationship between two or more numbers and variables.

Since the curve crosses the y-axis at y = 1, hence it is a cosine graph. It has a maximum of 1 and a minimum of negative 1, therefore the amplitude is 1

Also, the angular frequency = 2π * 1/5π = 0.4

The equation of the graph is given by y = cos(0.4x) and has an amplitude of 1

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Answer:

C

Step-by-step explanation:

Edge 2022

Answer:

  A = 90°

  B = 37°

  C = 53°

Step-by-step explanation:

Given three sides of a triangle, the Law of Cosines can be used to find the angles.

__

For angle A (the largest), we can use ...

  a² = b² +c² -2bc·cos(A)

Solving for A, we get ...

  A = arccos((b² +c² -a²)/(2bc)) = arccos((3² +4² -5²)/(2·3·4)) = arccos(0)

  A = 90°

We can use a similar equation for angle B:

  B = arccos((a² +c² -b²)/(2ac)) = arccos((25 +16 -9)/(2·5.4)) = arccos(4/5)

  B ≈ 37°

The sum of angles is 180°, so ...

  C = 180° -90° -37°

  C = 53°

Answer:

xy represents the diameter of the circle

Answer:

Aida did not correctly divide by the common factor to get (4 + 8).

Answer:

B). Aida did not correctly divide by the common factor to get (4 + 8).

Step-by-step explanation:

Aida applied the distributive property to write the equivalent expressions given as

15 + 21 = 3(4 + 8)

But Aida made a mistake.

Since to get the common factor of 15 and 21 she did not divide these numbers by 3 correctly.

In simple words by division of 3 in 15 and 21, we get 5 and 7 instead of 5 and 8.

Therefore, Aida did not correctly divide by the common factor to get (4 + 8). ⇒ option B is the correct answer.

Answer:

0

Step-by-step explanation:

slope = y2-y1/x2-x1

X1= 3 y1= -2

X2 = 9 y2= -2

slope= -2--2/9-3

slope= -2+2/6

slope= 0/6

slope= 0

Answer:

2x=x+30 [vertically opposite angle]

or,2x-x=30

:.x=30

Answer:

2x = x+30

2x - x = 30

X = 30

And goodluck

We will solve these through graphical way .

Find some coordinates

And

Find some coordinates

Graph both

The intersection points are

Answer:

45 cubic units

Step-by-step explanation:

Vtotal = 1/2 (2.5*3) * 6 *2

where

2.5 is the base

3 is the height

6 is the length

2 is the number of prisms

Answer:

The correct answer is 90 cubic units which is Option A.

Hope this helps you!!

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The solution to the amount of light bulbs Julia needs to sell to meet her quota is represented by the shaded area in graph X.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the incandescent light bulbs and y represent the fluorescent light bulbs. Therefore:

x + y > 100   (1)

Also:

2x + 5y ≥ 350    (2)

The solution to the amount of light bulbs Julia needs to sell to meet her quota is represented by the shaded area in graph X.

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